a parsimonious macroeconomic model for asset...

IntroductionModel

ResultsConclusionDiscussion

A Parsimonious Macroeconomic Model for AssetPricing

Guvenen, ECTA 2009Presented by: Rustom Irani, NYU Stern

November 23, 2009

Guvenen A Parsimonious Macroeconomic Model for Asset Pricing

IntroductionModel


Outline1 Introduction

MotivationContribution

2 ModelAssumptionsEquilibriumCalibration

3 ResultsAsset Pricing: Unconditional MomentsAsset Pricing: Conditional MomentsMacroeconomic QuantitiesMacro vs. Asset Pricing

4 Conclusion5 Discussion

Empirical EvidenceInterpreting MechanismRevisiting KL2008


IntroductionModel



Outline

1 IntroductionMotivationContribution

2 Model

3 Results

4 Conclusion

5 Discussion


IntroductionModel



Asset Prices and the Business Cycle

Getting asset prices and macroeconomic quantities in a GEmodel with production is hard:

1 Equity premium, risk-free rate level/volalility, predictability, etc.2 Counter-cyclical labor hours.

This paper proposes a new mechanism based on data:1 Limited Stock Market Participation: Until 1990’s about 2/3 of

individuals did not hold any stocks at all;2 Heterogeneity in EIS: Stock market participants have a higher

EIS (Blundell et al., REStud, 1994)1.

1EIS estimates are actually all over the place.Guvenen A Parsimonious Macroeconomic Model for Asset Pricing

IntroductionModel



Complementing Existing Literature

1 Heterogeneous trading technologies (Chien et al., WP, 2009):

Richer set of limits on access to financial markets in a moretractable endowment economy setting.

2 GE with production and recursive preferences (Kaltenbrunner& Lochstoer, WP, 2008):

Examines interaction of recursive prefs and technology shocks;KL2008 is the benchmark model for my discussion.

3 GE with production, recursive preferences and limitedparticipation (Gomes & Michaelides, RFS, 2008):

Similar, full-specified GE model that concludes limitedparticipation less important.


IntroductionModel


AssumptionsEquilibriumCalibration

Outline

1 Introduction

2 ModelAssumptionsEquilibriumCalibration

3 Results

4 Conclusion

5 Discussion


IntroductionModel



Environment

Neoclassical growth model with capital adjustment costs:

1 Discrete time, infinite horizon;

2 One firm with C-D technology and costly capital adjustment;3 Two consumer-types with E-Z preferences:

Different EIS and trading technology;Financial markets incomplete w.r.t. aggregate risk;No background/idiosyncratic risk.


IntroductionModel



Two Representative Consumers

Two groups of consumers differ along two dimensions:1 Trading technology (“limited participation”);2 Elasticity of intertemporal substitution.

“Stockholders” (i = h) vs.“Non-Stockholders” (i = n):

Fixed fraction of stockholders (µ);Stockholders less concerned about smoothing (EISh > EISn);Stockholders able to hold corporate bonds and stocks;Neither faces idiosyncratic risk.


IntroductionModel



Representative Consumers: Preferences

E-Z time-nonseparable preferences:

U it =

{(1− β)ui (Ct , 1− lt) + β

(Et

[(U i

t+1

)1−α]) 1−ρi1−α

} 1

1−ρi

Constant risk preferences:

α is (common) coefficient of relative risk aversion;1/ρi is (heterogenous) elasticity of intertemporal substitution.

Three specifications for intraperiod utility considered...


IntroductionModel



Two Representative Consumers: Preferences

1 “CONS”: u(c , 1− l) = c1−ρi

Labor supplied inelastically.


IntroductionModel




1 “CONS”: u(c , 1− l) = c1−ρi

2 “CD”: u(c , 1− l) =(cγ(1− l)1−γ)1−ρi

γ, ρi jointly pin down EIS, fraction of time devoted to work,and (Frisch) labor supply elasticity w.r.t. wages;Different ρi implies heterogeneity in Frisch elasticity;This is problematic and will be discussed later.


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1 “CONS”: u(c , 1− l) = c1−ρi

2 “CD”: u(c , 1− l) =(cγ(1− l)1−γ)1−ρi

3 “GHH”: u(c , 1− l) =(c − ψ l1+γ

1+γ

)1−ρi

MRS cons./leisure independent of level of consumption;Three parameters now pin down:

1. Labor supply elasticity (1/γ);2. EIS (1/ρi );3. ψ pins down the MRS between consumption and leisure.

Note that GHH is the preferred specification...


IntroductionModel



Technology

1 CRS production technology: Yt = ZtL1−αt Kα

t

2 TFP shocks: ln Zt = σε∑t

j=0 φjεt−j , εj ∼ i.i.d.N(0, 1)

Shocks transitory (φ < 1) and homoscedastic;Economy is stationary, i.e., not growing over time.

3 LOM capital: Kt+1 = (1− δ)Kt + Φ(

ItKt

)Kt

Φ(·) captures symmetric, convex capital adjustment costs;No adjustment cost if investing at SS rate.


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Representative Firm

1 Price-taking, homogenous-good producing firm;

2 Firm maximizes ex-dividend value s.t. LOM capital:

Pst = max{It+j ,Lt+j}

Et

∞∑j=1

βjΛht,t+jDt+j

Λht,t+j is representative stockholder’s IMRS.


IntroductionModel



Representative Firm: Dividends

Capital structure of firm:

1 One common share (equal to ex-dividend value of firm);

2 One perpetuity with face value χKss and coupon 1− P ft :

Same as rolling over 1-pd bond(s) with total face value χKss ,so bonds in constant supply with some price P f

t ;

=⇒ Dt = Yt −WtLt − It − χKss︸︷︷︸Redemption

+ P ft χKss︸︷︷︸

new issuance︸︷︷︸Net debt payments per period

Corporate debt introduced to model financial leverage (χ) onasset prices (see Danthine & Donaldson, REStud, 2002).


IntroductionModel



Consumer’s Problem: Non-Stockholder

Let B and Υ = (K ,B,Z ) denote bond holdings ofnon-stockholders and the aggregate state vector, resp.;

b′ and ω are bond holdings and financial wealth;

Non-stockholder’s problem can be formulated recursively as:

V n(ω; Υ) = maxc,l,b′

[(1− β)un(c, 1− l) + β

[EZV h

t+1(ω′; Υ′)1−α] 1−ρn

1−α

] 11−ρn

s.t. c + P f (Υ) · b′ ≤ ω + W (K ,Z) · lω′ = b′

b′ ≥ B

K ′ = ΓK (Υ) , B ′ = ΓB (Υ)


IntroductionModel



Consumer’s Problem: Stockholder

Stockholder’s problem can be formulated recursively as:

As before, but stock holdings s ′ 6= 0;

V h(ω; Υ) = maxc,l,b′,s′

[(1− β)uh(c, 1− l) + β

[EZV h

t+1(ω′; Υ′)1−α] 1−ρh

1−α

] 11−ρh

s.t. c + P f (Υ) · b′ + P s (Υ) · s ′ ≤ ω + W (K ,Z) · lω′ = b′ +

(P s (Υ′)+ D (Υ)

)· s ′

b′ ≥ B

K ′ = ΓK (Υ) , B ′ = ΓB (Υ)


IntroductionModel



Stationary Recursive Competitive Equilibrium

Decisions, prices, and LOMs for aggregate capital/bond holdings

of non-stockholders{

V i , c i , l i , bi ′ , s ′,W , I , L,Ps ,P f , ΓK , ΓB

}s.t.:

1 Optimality:

Given prices and LOMs, HH-types maximize utility;Given W and Λh, firm maximizes value.

2 Market Clearing:

Bond, stock and labor markets clear.

3 Aggregate Consistency:

LOMs are consistent with individual behavior/beliefs.


IntroductionModel



Baseline Calibration

Before I put parameters up, things to note:

1 Model is calibrated for 1880-1991:

This rationalizes fixed participation rate of 20%;Explains large empirical volatility of risk-free rate.

2 Model is solved at monthly frequency:

Approximate frequency of decision-making;Model AP moments time-aggregated to match annual data;Macro moments time-aggregated to match quarterly data.


IntroductionModel




Before I put parameters up, things to note:

1 Model is calibrated for 1880-1991:

2 Model is solved at monthly frequency:

3 All parameters are picked in standard fashion, except (α, σε):

Chosen to match Sharpe ratio of 0.25 (0.32 in data) & σ(∆y);Gives σε = 1.5% > 0.7% from post-war Solow residuals;Recall KL2008 calibrate (ξ, σε) to:

1 σ(∆c) & σ(∆c)/σ(∆y);2 Sharpe ratio of equity returns.


IntroductionModel





IntroductionModel


Asset Pricing: Unconditional MomentsAsset Pricing: Conditional MomentsMacroeconomic QuantitiesMacro vs. Asset Pricing

Outline

1 Introduction

2 Model

3 ResultsAsset Pricing: Unconditional MomentsAsset Pricing: Conditional MomentsMacroeconomic QuantitiesMacro vs. Asset Pricing

4 Conclusion

5 DiscussionGuvenen A Parsimonious Macroeconomic Model for Asset Pricing

IntroductionModel



Numbers: CONS (Inelastic Labor Supply) Model

Focus on CONS model, since intuition easier to explain;

Show robust to GHH preferences over (c , l) later.

Before I put AP moments up, things to note:1 When remove heterogeneity in EIS (=0.1), results broadly in

line with “LRR I” in KL2008;2 Results robust to changes in RRA of non-stockholders.


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Numbers: CONS (Inelastic Labor Supply) Model

Should this be the return on default-free corporate debt?Return


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Mechanism: Source of Equity Premium

1 Limited participation:

Concentrates capital income risk among stockholders;Firm’s returns are pro-cyclical;Stockholders demand premium for holding onto their firm.

2 Heterogeneity in EIS:

Non-stockholders face wage risk;They have greater desire for consumption-smoothing;They need bonds more, as other agent who can adjust stocks;During recession they want to reduce wealth, which requiresinterest payments by stockholders;Effect on stockholder’s consumption growth:

More volatile =⇒ increases unconditional MPR.

Can quantify this effect in the model...


IntroductionModel







Non-stockholders face wage risk;They have greater desire for consumption-smoothing;They need bonds more, as other agent who can adjust stocks;During recession they want to reduce wealth, which requiresinterest payments by stockholders;

Effect on stockholder’s consumption growth:




IntroductionModel







Non-stockholders face wage risk;They have greater desire for consumption-smoothing;They need bonds more, as other agent who can adjust stocks;During recession they want to reduce wealth, which requiresinterest payments by stockholders;Effect on stockholder’s consumption growth:




IntroductionModel




Variance decomposition of consumption growth:

ch =

[W +

θZK θL1−θ − I

µ

]︸︷︷︸

Ah

−(B − P f · B ′

)µ︸︷︷︸ah

=⇒ σ2[∆ ln ch

]≈ σ2

[∆

ah

Ah

]+ σ2

[∆ ln Ah

]+ 2σ

[∆ ln Ah,−∆

ah

Ah

]

Ah reflects wage and dividend income;

ah are net interest payments made by stockholder/firm-owner;

An, an reflect wage and interest payments for non-stockholder.


IntroductionModel




1 Interest payments constitute < 1% of average consumption;2 Stockholders have more volatile consumption growth:

In bad times (∆ ln Ah < 0) stockholders interest payments

increase (∆ ah

Ah > 0);Timing effect leads to greater consumption variance, largerunconditional MPR, and counter-cyclical MPR (more later).


IntroductionModel



Mechanism: Source of Equity PremiumValue function of Non-Stockholder


IntroductionModel



Mechanism: Source of Equity PremiumValue function of Stockholder


IntroductionModel



Mechanism: Review

1 Non-stockholder really wants to smooth consumption:

Saves in boom;Dissaves in bust.

2 In bust, wages drop so they roll over fewer bonds withfirm/stockholder;

3 Stockholder holds more bonds and must reduce consumption.


IntroductionModel



Mechanism: Low Volatility of Risk-Free Rate

1 Level of risk-free rate:

Will discuss later...

2 Volatility of the risk-free rate:

Lower than other studies and more so with endogenous labor;

Demand shocks move price less, given flatter demand curve:

1 Heterogeneity in EIS: A higher average EIS results in a flatterbond demand curve;

2 Limited participation: Equity acts as a partial substitute forstockholders, making their bond demand more elastic.


IntroductionModel



Mechanism: Low Volatility of Risk-Free Rate

1 Level of risk-free rate:

Will discuss later...

2 Volatility of the risk-free rate:

Lower than other studies and more so with endogenous labor;Demand shocks move price less, given flatter demand curve:

1 Heterogeneity in EIS: A higher average EIS results in a flatterbond demand curve;

2 Limited participation: Equity acts as a partial substitute forstockholders, making their bond demand more elastic.


IntroductionModel



Mechanism: Low Volatility of Risk-Free RateBond Supply and Demand

How to interpret second picture? Isn’t bond supply fixed?


IntroductionModel



Mechanism: Low Volatility of Risk-Free RateBond Supply and Demand

Bonds are in fixed positivesupply in this model;

Equilibrium demand curve willbe a weighted sum of these two;

It will be more elastic and henceprice will be less responsive todemand-side shocks.


IntroductionModel



Endogenous Labor Supply

With CD preferences over leisure-consumption, AP looks bad;

With GHH preferences, AP moments largely intact;

Less adjustment in labor to smooth consumption. Why?

No wealth effect on labor supply choice;Labor hours strongly pro-cyclical due to pro-cyclical wages and(calibrated) substitution effect.

Hence marginal utility still volatile when labor endogenous andMPR does not not fall too much.


IntroductionModel



Numbers: Return Predictability

Ps/D forecasts (excess?) returns in this model. Why?


IntroductionModel



Mechanism: Source of Return Predictability

1 Ps/D is pro-cyclical:

Following a Z -shock, Ps jumps immediately;Dividends and capital move by less due to adjustment costs:

(Dividends counter-cyclical? Ambiguous and not discussed.)

Hence, Cov [Z ,Ps/D] > 0.

2 Equity premium is counter-cyclical:Follows from counter-cyclical conditional variance of:

1 Consumption growth of stockholders (explained);2 Returns (not explained, obvious?).

Hence, interpreted as a price of risk (λht ), as opposed to a

quantity of risk (βt), effect...


IntroductionModel



Mechanism: Why is ERP Counter-Cyclical?

CONS model under CRRA preferences:

Et

[Rep

t+1

]≈ α · σt [R

ept+1]︸︷︷︸

(a)

·σt [∆ ln cht+1]︸︷︷︸

(b)

· ρt [∆ ln cht+1,R

ept+1]︸︷︷︸

(c)

Argument goes as follows:(a) Counter-cyclical, increases 18% boom to bust (ignore);(b) Counter-cyclical, increases 39% boom to bust;(c) Stable and close to one over cycle (β constant?).

σ2t

[∆ ln ch

t+1

]≈ σ2

t

[∆

aht+1

Aht+1

]+σ2

t

[∆ ln Ah

t+1

]+2σt

[∆ ln Ah

t+1,−∆ah

t+1

Aht+1

]

Counter-cyclical consumption growth volatility due to interestpayments by stockholders during recessions;

Counter-cyclical ERP follows from counter-cyclical MPR.


IntroductionModel



Numbers: Macro Moments


IntroductionModel



Quantities: Procylicality of Aggregate Hours

1 In RA models, labor hours are counter-cyclical:

In boom (↑ Z ), stock price increases;Wealth effect from stock ownership dominates substitutioneffect from increased wages;Labor hours drops during boom!


IntroductionModel




1 In RA models, labor hours are counter-cyclical:2 In present model, wealth effect only for stockholders:

Non-stockholders experience no wealth effect!In aggregate, hours will be procyclical!Won’t stockholders still have counter-cyclical labor hours?

Yes, for CD preferences;However, GHH preferences disentangle wealth effects fromlabor supply, which permits procyclical hours for both groups.


IntroductionModel




1 In RA models, labor hours are counter-cyclical:2 In present model, wealth effect only for stockholders:

Non-stockholders experience no wealth effect!In aggregate, hours will be procyclical!Won’t stockholders still have counter-cyclical labor hours?Yes, for CD preferences;However, GHH preferences disentangle wealth effects fromlabor supply, which permits procyclical hours for both groups.


IntroductionModel




1 In RA models, labor hours are counter-cyclical:

2 In present model, wealth effect only for stockholders:3 Volatility of labor hours?

GHH prefs sorts this out for same reason.


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Quantities: Wealth Distribution

Stockholders own 92% of aggregate wealth on average:

Big improvement on previous models;Cyclical nature of interest payments matters, not size!Why include housing wealth when report data?


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Assessing Trade-Off Between Macro & AP Moments


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Assessing Trade-Off Between Macro & AP Moments

Apparent “separation” between quantities and choice of RRA;

But, inconsistent with calibration strategy (p16.):

Alludes to trade-off between Sharpe ratio and σ(∆y);If so, the picture and discussion (p36.) are rather misleading.


IntroductionModel


Outline

1 Introduction

2 Model

3 Results

4 Conclusion

5 Discussion


IntroductionModel


Conclusion

1 General equilibrium model with production:

Limited stock market participation;Heterogeneity in EIS;GHH intraperiod utility.

2 Asset prices look good:

Volatile and counter-cyclical stockholder consumption growthgenerates volatile SDF and counter-cyclical MPR;Is stockholder consumption consistent with the data?Is the mechanism plausible?

3 Quantities appear to be fine too:

Mechanism yields procyclical aggregate hours;GHH preferences yield procyclical hours for stockholders.


IntroductionModel



Outline

1 Introduction

2 Model

3 Results

4 Conclusion

5 DiscussionEmpirical EvidenceInterpreting MechanismRevisiting KL2008


IntroductionModel



Empirical Evidence: Limited ParticipationDoes limited participation matter for asset pricing?

u = 1T

∑Tt=1 β

[∑i∈I c i

t+1∑i∈I c i

t

]−γ [Rt+1 − R f

t+1

]

Brav, Constantinides & Geczy (JPE,2002) investigate EE errors using thecomplete markets SDF above;

Only including individuals with largeassets (weakly) reconciles EPP;

V-J (JPE, 2002) does E-Z Euler eqnestimation and finds EISh >> EISn.


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Empirical Evidence: Stockholder ConsumptionIs stockholder consumption consistent with model?

Vissing-Jorgensen (AER, 2009) uses CEX and IRS data:

1 For 1982-2006, consumption growth of rich more exposed toaggregate consumption growth than average consumer:

This is consistent with previous findings.

2 Income exposure of rich is likely contributor to their higherconsumption exposure;

3 Key question: Is wage or non-wage income more exposed?

From 1929-82, non-wage income is more highly exposed;From 1982-2006, wage income is more highly exposed!


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Empirical Evidence: Stockholder Consumption1929-82: Non-wage income key!


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Empirical Evidence: Stockholder Consumption1982-2006: Wage income key!


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Empirical Evidence: Final Thoughts

1 Evidence that limited participation matters for asset pricing;2 Guvenen’s mechanism:

Income data consistent with mechanism, but no consumptiondata for this time period...Income data inconsistent with mechanism, for period withconsumption data!However, participation has increased from 1982-2006 (e.g.,Favilukis, WP, 2008), which might explain inconsistency.

3 Heterogeneity in EIS?

No clear evidence that stockholders have higher EIS;Results crucially depend on stockholders having PERU (later)...


IntroductionModel



How to Interpret Limited Participation in this Model?

Non-stockholders are allowed to hold corporate debt?!

Limited participation seems unnatural in this setup, but...

What if agents correspond to financial intermediaries?

More natural if heterogeneity in trading technologiescorresponds to trading restrictions on different financialintermediary-types...

What would asset pricing look like in this kind of model?Is this a more sensible framework for analyzing policy?

Useful direction for existing models with intermediaries?

Brunnermeier & Sannikov (WP, 2009);He & Krishnamurthy (WP, 2008).


IntroductionModel



A Parsimonious Model of the Firm?

Corporate debt to allow positive supply of bonds:

Leverage does not affect quantities;But, affects dividends and hence properties of asset returns.

Sensitivity of AP moments to bond market assumptions?

Bonds in zero net supply?Government debt (Gomes & Michaelides, RFS, 2008)?Risk of corporate default?

Modeling the firm’s capital structure:

Allow bonds issued on Kt not KSS (Jermann, JME, 1998);Allow issuance to become a control, i.e., χt .


IntroductionModel



A Parsimonious Model of the Firm?

What about cash/retained earnings?

e.g., Riddick & Whited (JF, 2009).

Implications for asset pricing?

Suppose costly equity financing over the cycle;Firm has incentive to smooth dividends!


IntroductionModel



KL2008: Some Questions

1 Transitory technology shocks and recursive preferences:Elasticity of intertemporal substitution:

1 EISh = 0.3 =⇒ prefer early resolution;2 EISn = 0.1 =⇒ prefer late resolution!

In KL2008, stockholders would like transitory tech. shocks, soMPR lower relative to CRRA model;Evident in EISh = EISn = 0.3 case...

AP Moments

2 Wages, dividends and cycle?

KL2008: wages too procyclical, so counter-cyclical dividends;Cyclical properties of dividends/wages not discussed here!


a parsimonious macroeconomic model for asset...

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